Problem: Simplify the following expression: $r = \dfrac{y^2 - 19y + 90}{y - 9} $
Explanation: First factor the polynomial in the numerator. $ y^2 - 19y + 90 = (y - 9)(y - 10) $ So we can rewrite the expression as: $r = \dfrac{(y - 9)(y - 10)}{y - 9} $ We can divide the numerator and denominator by $(y - 9)$ on condition that $y \neq 9$ Therefore $r = y - 10; y \neq 9$